Understand divisibility rules

Your child checks whether one number divides another using quick digit tests instead of long division.

• By 2 and 5: look only at the last digit
• By 4: the last two digits form a multiple of 4 (20 yes, 26 no)
• By 8: the last three digits form a multiple of 8 (420 no, 180 no)
• By 3 and 9: add the digits (2,105,233 has a digit sum of 16, so it is not divisible by 3)
• By 10: the number ends in 0

Deciding whether a number is a multiple of a given one is 4.OA.B.4; it prepares the common factor work of 6.NS.B.4.

Print page one and keep a pencil for the digit sums.

• For questions a to h, tick no or yes for each number.
• Question i has a single right choice; questions j and k can have several boxes ticked.
• Ask your child to say which rule they used before ticking, for example "the last two digits are 20, and 20 is a multiple of 4".

The second page shows the correct ticks in red, so a grown-up can check the whole sheet in a minute.

• Testing 4 and 8 the same way: 34,152,420 is divisible by 4 but not by 8, because 420 is not a multiple of 8.
• Reversing the 9 and 3 rule: every multiple of 9 is a multiple of 3, but not of 4 or 12, so "All of the above" is wrong.
• Looking at the wrong digit: 1,000,005 ends in 5, so it is not divisible by 10.

Next, use the rules to find the greatest common factor of two numbers.